In the fields of microsystem technology or nanotechnology as well as in precision mechanics or semiconductor assembly technology, various problems are posed such as the production of a surface with micro-mechanical structures, the finishing, grinding or polishing of a surface already partially produced, and the like. Here, conventional milling machines are at their technological limits because, even at high revolutions, the tip of the milling head removing the material is hardly able to remove any more material as a result of its tiny diameter.